Space-time multipath coding schemes for wireless communication systems

ABSTRACT

Space-time multipath (STM) coding techniques are described for frequency-selective channels, respectively. The described STM coded system guarantees full space-multipath diversity, and achieves large coding gains with high bandwidth efficiency. The techniques utilize a linearly coding technique, and incorporates subchannel grouping for application of the linear coding techniques. As a result, the techniques enable desirable tradeoffs between performance and complexity.

[0001] This application claims priority from U.S. Provisional Application Serial No. 60/374,886, filed Apr. 22, 2002, U.S. Provisional Application Serial No. 60/374,935, filed Apr. 22, 2002, U.S. Provisional Application Serial No. 60/374,934, filed Apr. 22, 2002, U.S. Provisional Application Serial No. 60/374,981, filed Apr. 22, 2002, U.S. Provisional Application Serial No. 60/374,933, filed Apr. 22, 2002, the entire contents of which are incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with Government support under Contract No. #CCR-0105612, awarded by the National Science Foundation, and Contract No. DAAD19-01-2-011 (University of Delaware Subcontract No. 497420) awarded by the U.S. Army. The Government may have certain rights in this invention.

TECHNICAL FIELD

[0003] The invention relates to communication systems and, more particularly, transmitters and receivers for use in wireless communication systems.

BACKGROUND

[0004] Broadband wireless communications call for high data-rate and high performance. When a symbol duration is smaller than a delay spread of the communication channel, frequency-selective propagation effects arise. Therefore, it is important for broadband wireless applications to design single- or multi-antenna systems that account for frequency-selective multipath channels.

[0005] Space-time (ST) coded multi-antenna transmissions over flat fading channels take advantage of spatial diversity offered by multiple transmit, and possibly receive, antennas, and have been relatively effective in combating fading, and enhancing data rates. ST coding for frequency-selective channels has also been pursued using single-carrier, or, multi-carrier transmissions. These code designs, however, do not guarantee full space-multipath diversity. Some of these code designs may guarantee full diversity, but as they rely on ST block codes, they incur rate loss of up to 50% when the number of transmit antennas is greater than two.

[0006] Some techniques call for delay diversity schemes that transmit one symbol over two antennas in different time-slots. Other techniques call for a so-termed phase sweeping transmission that creates time-variations to an originally slow-fading channel. Unfortunately, both analog phase-sweeping and delay-diversity approaches consume extra bandwidth, and they do not enjoy joint space-multipath diversity.

SUMMARY

[0007] In general, space-time multipath (STM) coding techniques are described for frequency-selective channels respectively. The described STM coded system guarantees full space-multipath diversity, and achieves large coding gains with high bandwidth efficiency. The techniques utilize a linearly coding technique, and incorporates subchannel grouping for application of the linear coding techniques. As a result, the techniques enable desireable tradeoffs between performance and complexity.

[0008] Digital phase sweeping techniques are described that enable maximum joint space-multipath diversity, and large coding gains. The techniques also afford a low-complexity modular implementation, when working with linearly precoded small-size groups of symbols. The techniques achieve a high rate of operation, in symbols per second per frequency, regardless of a symbol constellation used, and for any number of transmit-receive-antennae.

[0009] In one embodiment, a wireless communication device comprises a linear precoder, a power splitter, and a plurality of antennas. The linear precoder linearly precodes a data stream to produce a precoded data stream. The power splitter produces a plurality of mirrored precoded data streams from the precoded data streams. The plurality of antennas output waveforms in accordance with the mirrored precoded data streams.

[0010] In another embodiment, a method comprises applying a linear precoder to a data stream to form a precoded data stream, and splitting the power of the precoded data stream to produce a plurality of mirrored precoded data streams. The method further comprises transmitting the mirrored precoded data stream with respective antennas.

[0011] In another embodiment, a method comprises linearly encoding blocks of N symbols a data stream with a matrix to form a precoded data stream, wherein N is an integer function of the number of antennas N_(t) of a transmitter and an estimate number L of multi-path channels from the transmitter to a receiver. The method further comprises transmitting the precoded data stream with the antennas.

[0012] In another embodiment, a computer-readable medium comprises instructions to cause a programmable processor to apply a linear precoder to a data stream to form a precoded data stream. The instructions further cause the processor to split the power of the precoded data stream to produce a plurality of mirrored precoded data streams, and transmit the mirrored precoded data stream with respective antennas.

[0013] The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

[0014]FIG. 1 is a block diagram illustrating an exemplary telecommunication system in which a transmitter and receiver implement the space-time multipath techniques described herein.

[0015]FIG. 2 is a block diagram illustrating transmitter and receiver of FIG. 1 in further detail.

[0016]FIG. 2A illustrates how three multi-path channels can be viewed as one longer channel.

[0017]FIG. 3 is a flowchart that illustrates operation of the DPS-based space-time multipath techniques describe herein.

[0018]FIG. 4 is a block diagram illustrating the system of FIG. 1 as applied to multi-carrier space-time multipath communication.

[0019]FIG. 5 is a flowchart that illustrates application of the STM techniques to single-carrier systems.

[0020]FIG. 5A illustrates how the transmit blocks for each antenna in a multi-antenna system is a circularly delayed version of the previous ones.

[0021] FIGS. 6-8 are graphs that illustrate exemplary results of simulations of the described techniques.

DETAILED DESCRIPTION

[0022]FIG. 1 is a block diagram illustrating a telecommunication system 2 in which transmitter 4 communicates data to receiver 6 through wireless channels 8. In general, transmitter 4 employs space-time multipath (STM) coding techniques to combat frequency-selective characteristics of multi-path channels 8.

[0023] Transmitter 4 includes a plurality of antennas 20 ₁-20 _(Nt) for transmitting data to receiver 6. In particular, each antenna 20 outputs a waveform that propagates to receiver 6 through one or more multi-path communication channels. Transmitter 4 may output the waveforms using one of a number of conventional multi-user transmission formats, including Code Division Multiple Access (CDMA) and Orthogonal Frequency Division Multiplexing (OFDM). The former is an example of single-carrier multiple access scheme, while the latter is a multi-carrier scheme. OFDM has been adopted by many standards including digital audio and video broadcasting (DAB, DVB) in Europe and high-speed digital subscriber lines (DSL) in the United States. OFDM has also been proposed for local area mobile wireless broadband standards including IEEE802.11a, IEEE802g, MMAC and HIPERLAN/2.

[0024] The techniques described herein may be applied to uplink and/or downlink transmissions, i.e., transmissions from a base station to a mobile device and vice versa. Consequently, transmitters 4 and receivers 6 may be any device configured to communicate using a multi-user wireless transmission including a cellular distribution station, a hub for a wireless local area network, a cellular phone, a laptop or handheld computing device, a personal digital assistant (PDA), and the like.

[0025] As illustrated, transmitter 4 includes a serial-to-parallel (S/P) converter 12, a linear precoder 16, a plurality of parallel-to-serial (P/S) converters 19 ₁-19 _(Nt), and a plurality of transmit antennas 20 ₁-20 _(Nt). Receiver 6 includes a plurality of receive antennas 28 ₁-28 _(Nr), a plurality of serial-to-parallel (S/P) converters 32 ₁-32 _(Nr), and a decoder 36.

[0026] The information bearing symbols {s(n)} are drawn from a finite alphabet A_(s), and are parsed into blocks of size N×1:s(k):=[s(kN), . . . ,s((k+1)N−1)]^(T). The linear encoder maps s(k) to a codeword $\begin{matrix} {{{\nu_{\mu}(k)} = {{\sum\limits_{n = 0}^{N - 1}\quad {a_{n}^{(\mu)}\left\lbrack {s(k)} \right\rbrack}_{n}} + {b_{n}^{(\mu)}\left\lbrack {s(k)} \right\rbrack}_{n}^{*}}},{\forall{\mu \in \left\lbrack {1,N_{l}} \right\rbrack}},} & (1) \end{matrix}$

[0027] where a_(n)^((μ))  and  b_(n)^((μ))

[0028] are P×1 vectors. As symbols and their complex conjugates are linearly combined to form the codeword v_(μ)(k) transmitted from the μth antenna during the kth block interval, we call the mapping in (1), a linear ST coder.

[0029] The fading channel between the μth transmit- and the vth receive-antenna is assumed to be frequency-selective. The sampled baseband equivalent impulse response vector (that includes transmit- and receive-filters) is given by: $\begin{matrix} {{h^{({v,\mu})}:=\left\lbrack {{h^{({v,\mu})}(0)},\ldots \quad,{h^{({v,\mu})}(L)}} \right\rbrack^{T}},\quad {L:=\left\lfloor \frac{\tau_{\max}}{T_{s}} \right\rfloor},} & (2) \end{matrix}$

[0030] where τ_(max) is the maximum delay among all paths (delay spread), T_(s) is the symbol (equal to the sampling) period, and L denotes the maximum order of all (v,μ) channels. We assume ideal carrier synchronization, timing and symbol-rate sampling. At the vth receive-antenna, the symbol rate sampled sequence x_(v)(n) at the receive-filter output is $\begin{matrix} {{{x_{v}(n)} = {{\sum\limits_{\mu = 1}^{N_{t}}\quad {\sum\limits_{t = 0}^{L}\quad {{h^{({v,\mu})}(l)}{\upsilon_{\mu}\left( {n - l} \right)}}}} + {\zeta_{v}(n)}}},} & (3) \end{matrix}$

[0031] where v_(μ)(n):=[v_(μ)(k)]_(n), and ζ_(v)(n) is complex additive white Gaussian noise (AWGN) with mean zero, and variance σ_(ζ) ²=N₀.

[0032] The symbols x_(v)(n) are serial-to-parallel (S/P) converted to form P×1 blocks x_(v)(k):=[x_(v)(kP), . . . , x_(v)(kP+P−1)]^(T). The matrix-vector counter part of (3) is $\begin{matrix} {{{x_{v}(k)} = {{\sum\limits_{\mu = 1}^{N_{t}}\left( {{H^{({v,\mu})}{_{\mu}(k)}} + {H_{ibi}^{({v,\mu})}{_{\mu}\left( {k - 1} \right)}}} \right)} + {\zeta_{v}(k)}}},} & (4) \end{matrix}$

[0033] where H^((v,μ)) is a lower triangular Toeplitz matrix with first column [h^((v,μ))(0), . . . , h^((v,μ))(L), 0, . . . , 0]^(T), H_(ibi)^((v, μ))

[0034] is an upper triangular Toeplitz matrix with first row [0, . . . , 0,h^((v,μ))(L), . . . , h^((v,μ))(1)], and ζ_(v)(k) is the AWGN vector.

[0035] As described, system 2 is a linearly ST coded system capable of collecting the maximum joint space-multipath diversity as well as large coding gains with high bandwidth efficiency ∀N_(t)≧2.

[0036] We will first introduce criteria for designing our STM codes, based on these assumptions:

[0037] A1) Channel taps {h^((v,μ))(l)} are zero-mean, complex Gaussian random variables;

[0038] A2) Channel state information (CSI) is available at the receiver, but unknown to the transmitter;

[0039] A3) High SNR is considered for deriving the STM diversity and coding gains.

[0040] When transmissions experience rich scattering, and no line-of-sight is present, the central limit theorem validates A1). Notice that we allow not only for independent random channel coefficients, but also for correlated ones. A2) motivates the use of ST coding altogether. A3) is useful for asserting optimality of our designs, but is not required for the system operation.

[0041] Since our design will allow for correlated channels, we will denote the N_(t)N_(r)(L+1)×N_(t)N_(r)(L+1) channel correlation matrix and its rank, respectively, by:

R _(h) :=E[hh ^(H)], and r _(h):=rank(R _(h))≦N _(t) N _(r)(L+1),  (5)

[0042] where the N_(t)N_(r)(L+1)×1 channel vector is h:=[h^((1,1))(0), . . . ,h^((1,1))(L), . . . ,h^((1,N) ^(_(t)) ⁾(L), . . . ,h^((N) ^(_(r,)) ^(N) ^(_(t)) ⁾(L)]^(T). We summarize our performance results for the linearly coded systems as follows (see Appendix A for a proof):

[0043] Proposition 1 At high SNR, the maximum space-multipath diversity order achieved by maximum likelihood (ML) decoding any linearly coded ST transmission is: $\begin{matrix} {G_{d}^{\max} = {r_{h} \leq {N_{t}{{N_{r}\left( {L + 1} \right)}.}}}} & (6) \end{matrix}$

[0044] When the channel correlation matrix R_(h) has full rank, the maximum coding gain for any linearly ST coded system is $\begin{matrix} {{G_{c}^{\max} = {\left( {\det \left( R_{h} \right)} \right)^{\frac{1}{r_{h}}}\frac{d_{\min}^{2}}{N_{t}}}},} & (7) \end{matrix}$

[0045] where d_(min) is the minimum Euclidean distance of the constellation points in the finite alphabet A_(s).

[0046] Proposition 1 has the following qualities:

[0047] a) it derives in closed-form the maximum coding gain of all linearly coded ST transmissions;

[0048] b) it quantifies the diversity order G_(d) ^(max) for any linearly coded ST system, and can in fact be generalized to include also Galois-Field coded symbols;

[0049] c) it allows for correlated channels which is important since practical frequency-selective channels are correlated with an exponential power profile.

[0050]FIG. 2 is a block diagram illustrating additional embodiments of transmitter 4 and receiver 6 of FIG. 1. As illustrated, transmitter 4 and receiver 6 can be viewed as comprising three stages (pairs of encoders/decoders): an outer codec, a middle codec, and an inner codec. The outer codec includes a linear constellation precoding matrix Θ 50 of transmitter 4 and a corresponding decoder

(•) 66 of receiver 6. The middle codec implements our digital phase sweeping (DPS) scheme, and includes a power splitter 52 along with a set of DPS modules 54 to apply matrices {Φ_(μ)}_(μ = 1)^(Nt)

[0051] at transmitter 4, and a maximum ratio combiner (MRC) 64 of receiver 6. In this example, the inner codec performs orthogonal frequency division multiplexing (OFDM). Specifically, transmitter 4 includes modules 56 for performing an inverse fast Fourier transform (IFFT) operation (via the matrix F_(N) ^(H)), followed by modules 58 for performing cyclic-prefix (CP) insertion that can described as a matrix T_(cp). At receiver 6, the inner decoder performs two mirror operations: modules 60 remove the CP via a matrix T_(cp), and modules 62 perform the FFT. The CP-insertion and removal matrices are given, respectively as: $\begin{matrix} {{T_{cp}:=\begin{bmatrix} I_{cp} \\ I_{N} \end{bmatrix}},{R_{cp}:=\begin{bmatrix} 0_{N \times L_{cp}} & I_{N} \end{bmatrix}},} & (8) \end{matrix}$

[0052] where L_(cp) is the CP length, and I_(cp) denotes the last L_(cp) rows of I_(N). Based on these definitions, the input-output relationship from c_(μ) to y_(v) (see FIG. 2) can be expressed as: $\begin{matrix} {{y_{v} = {{\rho {\sum\limits_{\mu = 1}^{N_{t}}\quad {F_{N}R_{cp}H^{({v,\mu})}T_{cp}F_{N}^{\mathcal{H}}c_{\mu}}}} + \xi_{v}}},\quad {\forall{v \in {\left\lbrack {1,N_{r}} \right\rbrack.}}}} & (9) \end{matrix}$

[0053] where p:={square root}{square root over (N/(N+L_(cp)))}is a power-normalizing constant; the ξ_(v)'s are independent identically distributed (i.i.d.) AWGN vectors; and c_(μ) is the output of the middle encoder Φ_(μ). It is well-known that by (inserting) removing the CP and (I)FFT processing, a frequency-selective channel becomes equivalent to a set of flat-fading sub-channels. Mathematically, one can express this proper via: $\begin{matrix} {{{F_{N}R_{cp}H^{({v,\mu})}T_{cp}F_{N}^{\mathcal{H}}} = D_{H}^{({v,\mu})}},{\forall v},\quad \mu,{{{where}\quad D_{H}^{({v,\mu})}}:={{diag}\left\lbrack {{H^{({v,\mu})}(0)},\ldots \quad,{H^{({v,\mu})}\left( {N - 1} \right)}} \right\rbrack}},{{{with}\quad {H^{({v,\mu})}(n)}}:={\sum\limits_{l = 0}^{L}\quad {{h^{({v,\mu})}(l)}{^{{- {j2\pi}}\quad n\quad {l/N}}.}}}}} & (10) \end{matrix}$

[0054] Using (10), we can simplify (9) as: $\begin{matrix} {{y_{v} = {{\rho {\sum\limits_{\mu = 1}^{N_{t}}{D_{H}^{({v,\mu})}c_{\mu}}}} + \xi_{v}}},\quad {\forall{v \in {\left\lbrack {1,N_{r}} \right\rbrack.}}}} & (11) \end{matrix}$

[0055] Comparing (11) with (4), we confirm that the inner codec (OFDM) removes the inter-block interference (IBI), and also diagonalizes the channel matrices.

[0056] The middle encoder implements the phase sweeping techniques described herein. In a two transmit-antenna analog implementation, the signal of one antenna is modulated by a sweeping frequency f_(s) in addition to the carrier frequency f_(c)>>f_(s), that is present in both antennas. This causes bandwidth expansion by f_(s) Hz. In the following, we will derive a digital phase sweeping (DPS) encoder. Combined with OFDM, DPS will convert N_(t) frequency-selective channels, each having (L+1) taps, to a single longer frequency-selective channel with N_(t)(L+1) taps. Toward this objective, let us rewrite the diagonal channel matrix in (10) as: $\begin{matrix} {{D^{({v,\mu})} = {\sum\limits_{l = 0}^{L}\quad {{h^{({v,\mu})}(l)}D_{l}}}},{\forall{v \in \left\lbrack {1,N_{r}} \right\rbrack}},} & (12) \end{matrix}$

[0057] where D_(t):=diag[1,exp(−)j2πl/N), . . . ,exp(−j2πl(N−1)/N)]. Eq. (12) discloses that different channels may have different channel taps h^((v,μ))(l), but they all share common lags (l) that manifest themselves as common shifts in the FFT domain. Suppose that we shift the L+1 taps of each channel corresponding to one of the N_(t) transmit antennas so that all channel taps become consecutive in their delay lags. Then, we can view the N_(t) channels to each receive-antenna as one longer frequency-selective channel with N_(t)(L+1) taps. To realize this idea digitally, we select matrices {Φ_(μ)}_(μ = 1)^(N_(t))

[0058] as

Φ_(μ)=diag[1,e ^(jφμ) , . . . ,e ^(jφμ(N−1))], ∀μ∈[1,N _(t)],  (13)

[0059] where φ_(μ)=−2π(μ−1)(L+1)/N. Based on (12) and (13), we have that

D _(l)Φ_(μ) =D _(l+(μ−1)(L+1)) , ∀l∈[0,L],μ∈[1,N_(t)].  (14)

[0060] Let us now define the equivalent longer channel vector corresponding to the vth receive-antenna as:

h ^((v))=[(h ^((v,l)))^(T), . . . ,(h ^((v,N) ^(_(t)) ⁾)^(T)]^(T)  (15)

[0061] with the lth entry of h^((v)) given by: h^((v))(l)=h^((v,[t/(L+1)]+1)) (l mod (L+1)). Since h^((v)) in (15) has length N_(t)(L+1), we can view it as coming from a single frequency-selective channel. According to (14), we define the diagonal matrix of the longer equivalent channel as: $\begin{matrix} {D_{H}^{({v,})}:={{\sum\limits_{\mu = 1}^{N_{t}}{D_{H}^{({v,\mu})}\Phi_{\mu}}} = {\sum\limits_{l = 0}^{{N_{t}{({L + 1})}} - 1}\quad {{h^{({v,})}(l)}{D_{l}.}}}}} & (16) \end{matrix}$

[0062] In essence, the DPS matrix Φ_(μ) shifts the delay lags of the μth channel (c.f. (14)) from [0,L] to [(μ−1)(L+1)·μ(L+1)−1]. For example, when μ=1, Φ₁=I_(N) and then D^((v,1))Φ₁=diag({square root}{square root over (N)}F_(0:L)h^((v,1)), where F_(0:L) denotes the first L+1 columns of F_(N). When μ=2, D^((v,2))Φ₂=(diag({square root}{square root over (N)}F_((L+1):(2L+1))h^((v,2)), where F_((L+1):(2L+1)) denotes the (L+1)st up to (2L+1)st columns of F_(N). Proceeding likewise with all N_(t) DPS matrices, we can also obtain (16). FIG. 2A illustrates how three multi-path channels can be viewed as one longer channel.

[0063] We summarize this observation in the following:

[0064] Property 1: DPS converts the N_(t) transmit-antenna system, where each frequency-selective channel has L+1 taps, to a single transmit-antenna system, where the equivalent channel has N_(t)(L+1) taps.

[0065] Remark 1 To avoid overlapping the shifted bases, we should make sure that N>N_(t)(L+1). From the definition of the channel order L:=[τ_(max)/T_(s)], we have that for fixed τ_(max) and N, we can adjust the sampling period T_(s) to satisfy this condition, or equivalently, for fixed T_(s) and τ_(max), we can adjust the block size N. Since for each receive-antenna we have N_(t)(L+1) unknown channel tape corresponding to N_(t) channels every N symbols, this condition guarantees that the number of unknowns is less than the number equations. Therefore, even from a channel estimation point of view, this condition is justifiable.

[0066] Using the DPS matrices (13), we will normalize (power split) Φ_(μ)u to obtain the middle encoder output c_(μ)=Φ_(μ)u/{square root}{square root over (N_(t))}, ∀μ∈[1,N_(t)]. The input-output relationship (11) can then be rewritten as [c.f. (16)]: $\begin{matrix} {{y_{v} = {{\frac{\rho}{\sqrt{N_{t}}}D_{H}^{(v)}u} + \xi_{v}}},\quad {\forall{v \in {\left\lbrack {1,N_{r}} \right\rbrack.}}}} & (17) \end{matrix}$

[0067] To collect the full diversity and large coding gains, we not only need to design the transmitter properly, but we must also select a proper decoder at the receiver. Since the received blocks y_(v) from all N_(r) receive-antennas contain the information block s, we need to combine the information from all received blocks to decode s. To retain decoding optimality, we perform maximum ratio combining (MRC). The MRC amounts to combining {y_(v)} in (17) to form z=Gy using the matrix $\begin{matrix} {{G = {\left( {\sum\limits_{v = 1}^{N_{r}}{D_{H}^{(v)}\left( D_{H}^{(v)} \right)}^{*}} \right)^{- \frac{1}{2}}\left\lbrack {\left( D_{H}^{(1)} \right)^{*}\cdots \quad \left( D_{H}^{(N_{r})} \right)^{*}} \right\rbrack}},{{{and}\quad y} = {\left\lbrack {y_{1}^{T},\ldots \quad,y_{N_{r}}^{T}} \right\rbrack^{T}.}}} & (18) \end{matrix}$

[0068] Existence of the inverse in (18), requires the channels D_(H)^((v))

[0069] to satisfy the coprimeness condition: $\begin{matrix} {{\det \left( {\sum\limits_{v = 1}^{N_{r}}{D_{H}^{(v)}\left( D_{H}^{(v)} \right)}^{*}} \right)} \neq 0.} & \text{A4)} \end{matrix}$

[0070] Assumption A4) is more technical rather than restrictive, since it requires that the equivalent channels do not have common channel nulls. Indeed, for random channels, A4) excludes an event with probability measure zero.

[0071] With the MRC of (18), the vector z is given by [c.f. (17)]: $\begin{matrix} {{z = {{\frac{\rho}{\sqrt{N_{t}}}\left( {\sum\limits_{v = 1}^{N_{r}}\quad {D_{H}^{(v)}\left( D_{H}^{(v)} \right)}^{*}} \right)^{\frac{1}{2}}u} + \eta}},{{{where}\quad \eta}:={{G\left\lbrack {\zeta_{1}^{T},\ldots \quad,\zeta_{N_{r}}^{T}} \right\rbrack}^{T}.}}} & (19) \end{matrix}$

[0072] Under A4), it can be verified that G satisfies GG^(H)=1. Since the ζ_(v)'s are uncorrelated AWGN blocks, the noise vector η retains their whiteness. From (19) and (11), we deduce that the middle codec has converted a multi-input multi-output system into a single-input single-output system with longer impulse response.

[0073] To achieve full diversity, we still need to design the outer codec properly. If there is no precoding, i.e., u=s, the diversity order is one even if maximum likelihood decoding is used. To enable the full N_(t)(L+1) space-multipath diversity established by Proposition 1, we also need to design the precoder Θ judiciously.

[0074] As illustrated in FIG. 2, the outer codec utilizes linear constellation precoding. In particular, we design Θ using a Grouped Linear Constellation Precoding (GLCP) scheme described in U.S. Provisional Application Serial No. 60/374,935, entitled “LINEAR CONSTELLATION PRECODING FOR FADING COMMUNICATION CHANNELS,” filed Apr. 22, 2002, and U.S. patent application Ser. No.______, filed Apr. 21, 2003, entitled “WIRELESS COMMUNICATION SYSTEM HAVING LINEAR ENCODER,” the entire contents of which are incorporated herein by reference. GLCP provides a means of reducing decoding complexity without sacrificing diversity or coding gains. To apply GLCP, we select the transmitted block size N=N_(g)N_(sub), and demultiplex the information vector s into N_(g) groups: {s_(g)}_(g = 0)^(N_(g) − 1),

[0075] with each group having length N_(sub); e.g., and the gth group contains the symbols collected in a vector s_(g) as follows:

s _(g) =[[s] _(N) _(sub) _(g) ; . . . , [s] _(N) _(sub) _((g+1)−1)]^(T) , ∀g∈[0,N _(g)−1].  (20)

[0076] Correspondingly, we define the gth linearly precoded group as:

u _(g)=Θ_(sub) s _(g) , ∀g∈[0,N _(g)−1],  (21)

[0077] where Θ_(sub) is an N_(sub)×N_(sub) matrix. To enable the maximum diversity, we select Θ_(sub) from the algebraic designs of [24]. The overall transmitted block u consists of multiplexed sub-blocks {u_(g)}_(g = 0)^(N_(g) − 1)

[0078] as follows:

u=[[u ₀]₀ . . . [u _(N) _(g) ⁻¹]₀ ; . . . [u ₀]_(N) _(sub) ⁻¹ . . . [u _(N) _(g) ⁻¹]_(N) _(sub) _(−1]) ^(T).  (22)

[0079] It is not difficult to verify that u can be obtained from {u_(g)}_(g = 0)^(N_(g) − 1,)

[0080] via a block interleaver with depth N_(sub). Equivalently, it turns out that u can be related to s as $\begin{matrix} {{u = {\Theta \quad s}},{{{with}\quad \Theta}:=\begin{bmatrix} {I_{N_{g}} \oplus \theta_{1}^{T}} \\ \vdots \\ {I_{N_{g}} \oplus \theta_{N_{sub}^{T}}} \end{bmatrix}},} & (23) \end{matrix}$

[0081] where θ_(m) ^(T) is the mth row of Θ_(sub). Equations (20)-(22), or equivalently (23), summarize how the GLCP encoder is applied to our DPS based STM design.

[0082] To decode LCP transmissions, we split z in (19) into N_(g) groups: $\begin{matrix} {{z_{g} = {{\frac{\rho}{\sqrt{N_{t}}}D_{H,g}\Theta_{sub}s_{g}} + \eta_{g}}},{\forall{g \in \left\lbrack {0,{N_{g} - 1}} \right\rbrack}},} & (24) \end{matrix}$

[0083] where z_(g):=[[z]_(g), [z]_(N) _(sub) _(+g); . . . , [z]_(N) _(sub) _((N) _(g) _(−1)+g)]^(T), D_(H,g) is the corresponding diagonal sub-matrix from $\left( {\sum\limits_{v = 1}^{N_{r}}\quad {D_{H}^{(v)}\left( D_{H}^{(v)} \right)}^{*}} \right)^{\frac{1}{2}}$

[0084] for the gth group; and similarly defined, η_(g) is the corresponding AWGN vector from η. Maximum likelihood (ML) decoding of z can, for example, be implemented by applying a Sphere Decoding (SD) algorithm of sub-blocks z_(g) of small size N_(sub). Compared to the exponentially complex ML decoder, the SD offers near-ML performance at complexity of order Ο(N_(sub)^(α)).

[0085] The SD complexity depends on the block size N_(sub), but unlike ML, it is independent of the constellation size.

[0086]FIG. 3 is a flowchart that illustrates operation of the DPS-based space-time multipath techniques describe herein. For exemplary purposes, the operation is described in reference to FIG. 2.

[0087] Given N_(t), N_(r) and L, transmitter 4 selects the number of groups Ng, and the corresponding group size N_(sub) depending on affordable complexity; and selects N=N_(g)N_(sub)>N_(t)(L+1) (step 70).

[0088] Linear precoder 16 applies the N_(sub)×N_(sub) linear constellation precoder Θ_(sub) to form a precoded data stream, i.e., the precoded vectors u, according to equations (20)-(22) (step 72). Power splitter 52 splits the power of u to form mirrored precoded data streams ^(u/{square root}{square root over (N_(t))} (step 74).)

[0089] DPS modules 54 apply DPS via Φ_(μ) to u, and obtain c_(μ)=Φ_(μ)u/{square root}{square root over (N_(t))},∀μ∈[1,N_(t)] (step 76). In particular, transmitter 4 estimates a delay lag for each of a plurality of multi-path channels from transmitter 4 to receiver 6, and computes a single channel vector from the estimated delay lags for the channels. DPS modules 54 (FIG. 2) processes the mirrored precoded data streams with the single channel vector to shift the delay lag of each of the channels so that channel taps become consecutive. Finally, transmitter 4 modulates each block c_(μ) using OFDM and generates a transmission waveform via transmission antennas 20 (step 78).

[0090] Receiver 6 receives a waveform via receive antennas 28, and demodulates the received waveform (step 80). Next, receiver 6 performs MRC of blocks from all of the receive antennas 28 as in (19) (step 82). Finally, receiver 6 splits the MRC output block into Ng groups (step 84), and implements a scheme, e.g., ML or Sphere, to decode each reduced size group as in equation (24) to provide the estimated data (step 86).

[0091] The diversity gain for the STM techniques described herein can be summarized in the following proposition:

[0092] Proposition 2 The maximum achievable space-multipath diversity order G_(d)^(max) = r_(h)

[0093] is guaranteed by our STM design, provided that we select N_(sub)≧N_(t)(L+1). When the channel correlation matrix R_(h) has full rank r_(h)=N_(r)N_(t)(L+1), our STM design achieves (as p={square root}{square root over (N/(N+L_(cp)))}→1) the maximum possible coding gain among all linearly coded ST systems. The coding gain of our STM scheme is given in closed form by: $G_{c} = {\left( {\det \left( R_{h} \right)} \right)^{\frac{1}{r_{h}}}d_{\min}^{2}{N/{\left( {N_{t}\left( {N + L_{cp}} \right)} \right).}}}$

[0094] The transmission rate of our design is N/(N+L_(cp)) symbols/sec/Hz, ∀N_(t),N_(r).

[0095] Our choice of the group size N_(sub) determines whether the maximum diversity order can be achieved. In fact, N_(sub) offers flexibility to tradeoff between performance and decoding complexity. When N_(sub)≦N_(t)(L+1), as N_(sub) decreases, the decoding complexity decreases, while at the same time, the diversity order decreases. By adjusting N_(sub), we can balance the affordable complexity with the required performance. This is important because for a large number of transmit-receive antennae, or large delay spreads one does not have to strike for diversity orders greater than four (which in fact show up for unrealistically high SNRs). In such cases, small N_(sub) sizes (2 or 4) are recommended because they allow for ML decoding with reduced complexity.

[0096] Corollary 1 When R_(h) has full rank; i.e., r_(h)=N_(t)N_(r)(L+1), our STM achieves diversity order G_(d)=N_(sub)N_(r) when N_(sub)<N_(t)(L+1) and G_(d)=N_(t)N_(r)(L+1) when N_(sub)≧N_(t)(L+1).

[0097] In the context of frequency-selective channels, the STM techniques described herein offer the following attractive features:

[0098] 1) STM enables full space-multipath diversity gain r_(h)≦N_(t)N_(r)(L+1);

[0099] 2) STM guarantees large coding gain;

[0100] 3) STM is flexible to strike desirable performance-complexity tradeoffs;

[0101] 4) compared with ST block codes, STM suffers no rate loss ∀N_(t),N_(r);

[0102] 5) compared with ST trellis codes, STM affords easier code construction and constellation-independent decoding complexity.

[0103] Table 1 illustrates quantitative comparisons of the space-time multipath (STM) techniques described herein with existing alternatives for both single- and multi-carrier. TABLE I schemes STM STF [13] ZP-only [25] DD [6] DD [15] N_(t) ∀N_(t) ∀N_(t) ∀N_(t) 2 2 N_(r) ∀N_(r) ∀N_(r) ∀N_(r) 1 1 decoder SD SD VA VA MF complexity Ο((N_(t)(L + 1))^(α))

Ο((L + 1)^(α))

Ο((log _(s))^((L + 1)))

/ / G_(d) N_(t)N_(r)(L + 1) N_(t)N_(r)(L + 1) N_(t)N_(r)(L + 1) 2(L + 1) L + 2 G_(c) $\frac{{Nd}_{\min}^{2}}{\left( {N + L_{cp}} \right)N_{t}}$

$\frac{{Nd}_{\min}^{2}}{\left( {N + L_{cp}} \right)N_{t}}$

$\frac{d_{\min}^{2}}{N_{t}}$

/ / rate (s/s/Hz) $\frac{N}{N + L_{cp}}$

$\frac{N}{N + L_{cp}}r_{stbc}$

$\frac{N}{N + L_{cp}}r_{stbc}$

$\frac{N}{N + {2L} + 1}$

$\frac{N}{N + L + 2}$

[0104] In Table 1, SD, VA, and MF stand for sphere decoding, Viterbi's algorithm, and matched filter, respectively; and R_(stbc) denotes a rate of the orthogonal ST block code.

[0105] The STM coding techniques may be applied to both single- and multi-carrier systems. The following provides further details regarding multi-carrier systems.

[0106] Recalling Φ_(μ) in (13), it is easy to show using the IFFT matrix definition that $\begin{matrix} {{{F_{N}^{\mathcal{H}}\Phi_{\mu}}:={{\begin{bmatrix} f_{0}^{T} \\ \vdots \\ f_{N - 1}^{T} \end{bmatrix}\Phi_{\mu}} = \begin{bmatrix} f_{{({\mu - 1})}{({L + 1})}}^{T} \\ \vdots \\ f_{{{({\mu - 1})}{({L + 1})}} - 1}^{T} \end{bmatrix}}},} & (25) \end{matrix}$

[0107] where f_(n) ^(T) is the nth row of F_(N) ^(H). Eq. (25) shows that left multiplying matrix Φ_(μ) by the IFFT matrix F_(N) ^(H) is equivalent to permuting the rows of F_(N) ^(H) circularly. Therefore, there exists an N×N permutation matrix P_(μ) such that

P_(μ)F_(N) ^(H)=F_(N) ^(H)Φ_(μ), ∀μ∈[1,N_(t)],  (26)

[0108] where $\begin{matrix} {P_{\mu}:={\begin{bmatrix} 0 & I_{{({\mu - 1})}{({L + 1})}} \\ I_{N - {{({\mu - 1})}{({L + 1})}}} & 0 \end{bmatrix}\quad {\forall{\mu \in {\left\lbrack {1,N_{t}} \right\rbrack.}}}}} & (27) \end{matrix}$

[0109] Using the property in (26), we can rewrite (9) as (see also FIG. 4) $\begin{matrix} {y_{v} = {{\frac{\rho}{\sqrt{N_{2}}}{\sum\limits_{p = 1}^{N_{t}}{F_{N}R_{cp}H^{({v,F})}T_{cp}P_{\mu}F_{N}^{\mathcal{H}}u}}} + {\xi_{\mu}\quad {\forall{v \in {\left\lbrack {1,N_{r}} \right\rbrack.}}}}}} & (28) \end{matrix}$

[0110] Defining {overscore (u)}:=F_(N) ^(H)u, and based on the definition of P_(μ) in (27), we find that

{square root}{square root over (N_(t))} c _(μ) =P _(μ) {overscore (u)}=[[{overscore (u)}]_([μ−1][L+1]), . . . ,[{overscore (u)}]_(N), . . . ,[{overscore (u)}]_([μ−1)(L+1)]−1)]^(T).  (29)

[0111] We infer from (29) that the transmitted blocks c_(μ) on the μth antenna is a circularly delayed version of the previous ones (see FIG. 5A). We summarize the analysis above as follows:

[0112] Property 2: A DPS-based transmission (FIG. 2) is equivalent to a circular delay diversity (CDD) transmission given in (FIG. 4).

[0113] Unlike conventional delay diversity designs, the DPS-based (or equivalently CDD-based) STM scheme described herein does not sacrifice bandwidth efficiency. Compared to the STM design in FIG. 2, the equivalent multi-carrier system of FIG. 4 has lower complexity because it requires only one IFFT operation (instead of N_(t) IFFT operations).

[0114]FIG. 5 is a flowchart that illustrates application of the STM techniques to single-carrier systems. For exemplary purposes, the operation is described in reference to FIG. 1.

[0115] Given N_(t), N_(r) and L, depending on affordable complexity, transmitter 4 selects a block size N>N_(t)(L+1) (step 100).

[0116] Transmitter 4 applies a N×N linear constellation precoder Θ according to (25) and forms precoded vectors u=Θs (step 102). Transmitter 4 splits the power of u to form ^(u/{square root}{square root over (N_(t))} (step 104).)

[0117] Transmitter 4 applies a circular delay (via P_(μ)) per antenna, to obtain c_(μ)=P_(μ)u/{square root}{square root over (N_(t))}, ∀μ∈[1,N_(t)]. (step 106). Finally, transmitter 4 inserts CP, and modulates each block c_(μ) to generate a transmission waveform (step 108).

[0118] Receiver 6 receives a waveform, removes the CP, and applies an FFT to demodulate each block of the received data stream (step 110). Next, receiver 6 performs MRC of blocks from all of the receive antennas 28 as is (19) (step 112). Finally, receiver 6 implements a scheme, e.g., ML decoding, sphere decoding, Viterbi's algorithm, to decode each reduced size group as in (24) to provide the estimated data (step 116).

EXAMPLES

[0119] Test case 1: To illustrate the effects of multipath diversity, we first simulated the performance of the STM techniques with N_(t)=2 transmit and N_(r)=1 receive antennae in the presence of multi-ray channels with different channel orders L=0, 1, 2. The channel taps were i.i.d. Gaussian random variables with zero mean and variance 1/(L+1) were used. The CP length was L_(cp)=L. QPSK modulation was selected. The sub-block size was N_(sub)=N_(t)(L+1) and the number of sub-blocks was N_(g)=6. The information block length was N=N_(sub)N_(g). FIG. 6 depicts the average bit error rate (BER) versus SNR of the STM techniques. We observe that as the channel order L increased, the STM techniques achieved higher diversity order.

[0120] Test case 2: To illustrate the tradeoff of diversity with complexity, we adjusted the group size N_(sub). The parameters and the channel model were the same as in Test case 1, except that the channel order L was fixed as L=2. In this case, G_(d)^(max) = 6.

[0121]FIG. 7 confirms that as N_(sub) decreases, the achieved diversity decreases. Since the channel correlation matrix R_(h) has full rank, the achieved diversity order is N_(sub).

[0122] Comparing the slopes of BER curves in FIG. 6 and FIG. 7 confirms our result. Note that decoding complexity also decreases as N_(sub) decreases. This shows that when the product N_(t)L is large, we can select N_(sub) small to lower complexity.

[0123] Test case 3: In this example, we set L=2, N_(r)=1, and N_(t)=2,4. The channel taps are independent and satisfy an exponentially decaying power profile. When N_(t)=2, we selected QPSK for both STM and STF. From FIG. 8, we infer that STF outperforms STM about 1 dB, while having lower computational complexity. When N_(t)=4, to maintain the same transmission rate, we selected BPSK for our STM and QPSK for STF, because STF uses the block code that has rate ½ symbols/sec/Hz. From FIG. 8, we observe that observe that our STM techniques outperforms the STF by about 3 dB.

[0124] Various embodiments of the invention have been described. The described techniques can be embodied in a variety of receivers and transmitters including base stations, cell phones, laptop computers, handheld computing devices, personal digital assistants (PDA's), and the like. The devices may include a digital signal processor (DSP), field programmable gate array (FPGA), application specific integrated circuit (ASIC) or similar hardware, firmware and/or software for implementing the techniques. If implemented in software, a computer readable medium may store computer readable instructions, i.e., program code, that can be executed by a processor or DSP to carry out one of more of the techniques described above. For example, the computer readable medium may comprise random access memory (RAM), read-only memory (ROM), non-volatile random access memory (NVRAM), electrically erasable programmable read-only memory (EEPROM), flash memory, or the like. The computer readable medium may comprise computer readable instructions that when executed in a wireless communication device, cause the wireless communication device to carry out one or more of the techniques described herein. These and other embodiments are within the scope of the following claims. 

1. A wireless communication device comprising: a linear precoder that linearly precodes a data stream to produce a precoded data stream; a power splitter to produce a plurality of mirrored precoded data streams from the precoded data streams; and a plurality of antennas to output waveforms in accordance with the mirrored precoded data streams.
 2. The wireless communication device of claim 1, further comprising a plurality of digital phase sweeping modules that compute a single channel vector from estimates of delay lags for each of a plurality of multi-path channels to a receiver, and process the mirrored precoded data streams with the single channel vector to shift the delay lag of each of the channels so that channel taps within the mirrored precoded data streams become consecutive.
 3. The wireless communication device of claim 1, the linear precoder comprises a linear constellation precoder.
 4. The wireless communication device of claim 1, wherein the linear precoder applies a unitary matrix to blocks of M symbols of the encoded data stream.
 5. The wireless communication device of claim 1, further comprising a plurality of modulators to modulate each mirrored precoded data stream and produce the waveforms for transmission with the respective antennas.
 6. The wireless communication device of claim 1, wherein the waveforms are multi-carrier waveforms.
 7. The wireless communication device of claim 1, wherein the waveforms are single-carrier waveforms.
 8. The wireless communication device of claim 1, wherein the linear precoder applies a matrix to symbol blocks of the data stream, wherein each block contains N symbols, and the matrix has a size that is an integer function of the number of antennas N_(t) and the estimate number (L) of multi-path channels.
 9. The wireless communication device of claim 8, wherein N>N_(t)*L.
 10. The wireless communication device of claim 8, wherein the linear precoder divides each of the blocks of the data stream into N_(g) groups, where each group has N_(sub) symbols, and N_(sub) is an integer function of the number of antennas and the estimate number of multi-path channels.
 11. The wireless communication device of claim 10, wherein N_(sub)≧N_(t)*L.
 12. The wireless communication device of claim 10, wherein the matrix applied by the linear precoder has a size of N_(sub)×N_(sub).
 13. The wireless communication device of claim 10, further comprising modules to apply a permutation matrix to each of the precoded data streams to permute the symbol blocks within the mirrored precoded data streams.
 14. The wireless communication device of claim 13, wherein the antennas transmit a multi-carrier waveform directly from the mirrored precoded data streams.
 15. The wireless communication device of claim 14, wherein the wireless communication device transmits an orthogonal frequency division multiplexing waveform (OFDM) with each of the antennas directly from the mirrored precoded data streams without applying an inverse fast Fourier transform (IFFT) to each of the mirrored precoded data streams. 16 The wireless communication device of claim 15, wherein linear precoder applies a linear constellation precoding matrix having a dimensions of N×N to each of the blocks of the data stream to form the precoded data stream, and the wireless communication device transmits the mirrored precoded data streams as single-carrier waveforms.
 17. The wireless communication device of claim 1, wherein the wireless communication device comprises one of a base station and a mobile device.
 18. A method comprising: applying a linear precoder to a data stream to form a precoded data stream; splitting the power of the precoded data stream to produce a plurality of mirrored precoded data streams; and transmitting the mirrored precoded data stream with respective antennas.
 19. The method of claim 18, further comprising: estimating a delay lag for each of a plurality of multi-path channels from the transmitter to a receiver; computing a single channel vector from the estimated delay lags for the channels; and processing the mirrored precoded data streams with the single channel vector to shift the delay lag of each of the channels so that channel taps within the mirrored precoded data streams become consecutive.
 20. The method of claim 18, wherein applying a linear precoder comprises applying a linear constellation precoder.
 21. The method of claim 18, wherein transmitting the mirrored precoded data streams comprises modulating each mirrored precoded data stream to produce a set of waveforms for transmission with the respective antennas.
 22. The method of claim 21, wherein the waveforms are multi-carrier waveforms.
 23. The method of claim 21, wherein the waveforms are single-carrier waveforms.
 24. The method of claim 18, wherein applying a linear precoder comprises: selecting a block size N as a function of the number of antennas N_(t) and an estimate number L of multi-path channels to a receiver; and applying a matrix to symbol blocks of the data stream, wherein the matrix has a size that is selected as a function of the number of antennas and the estimate number of multi-path channels.
 25. The method of claim 24, wherein N>N_(t)*L.
 26. The method of claim 24, wherein applying a linear precoder comprises: dividing each of the blocks of the data stream into N_(g) groups, where each group has N_(sub) symbols, and N_(sub) is selected as a function of the number of antennas and the estimate number of multi-path channels; and applying the matrix to each of the symbol groups within the blocks, wherein the matrix has a dimension that is a function of the number of symbols N_(sub) within the groups.
 27. The method of claim 26, wherein N_(sub)≧N_(t)*L.
 28. The method of claim 26, wherein a size of the matrix is N_(sub)×N_(sub).
 29. The method of claim 24, wherein transmitting the mirrored precoded data streams comprises: applying a permutation matrix to each of the precoded data streams to permute the blocks within the precoded data streams; and transmitting a multi-carrier waveform with each of the antennas directly from the permuted precoded data streams.
 30. The method of claim 29, wherein transmitting a multi-carrier waveform comprises transmitting an orthogonal frequency division multiplexing waveform (OFDM) with each of the antennas directly from the permuted precoded data streams without applying an inverse fast Fourier transform (IFFT) to each of the precoded data streams. 31 The method of claim 30, wherein applying a matrix comprises applying a matrix having a dimensions of N×N to each of the blocks of the data stream to form the precoded data stream.
 32. The method of claim 18, wherein transmitting the mirrored precoded data streams comprises transmitting each of the mirrored precoded data streams as a single-carrier waveform with a respective one of the antennas.
 33. A computer-readable medium comprising instructions to cause a programmable processor of a wireless communication device to: apply a linear precoder to a data stream to form a precoded data stream; split the power of the precoded data stream to produce a plurality of mirrored precoded data streams; and transmit the mirrored precoded data stream with respective antennas.
 34. The computer-readable medium of claim 33, further comprising instructions to cause the programmable processor to: estimate a delay lag for each of a plurality of multi-path channels from the transmitter to a receiver; compute a single channel vector from the estimated delay lags for the channels; and process the mirrored precoded data streams with the single channel vector to shift the delay lag of each of the channels so that channel taps within the mirrored precoded data streams become consecutive.
 35. The computer-readable medium of claim 33, further comprising instructions to cause the programmable processor to: select a block size N as a function of the number of antennas N_(t) and an estimate number L of multi-path channels to a receiver; and apply a matrix to symbol blocks of the data stream, wherein the matrix has a size that is selected as a function of the number of antennas and the estimate number of multi-path channels.
 36. A method comprising: linearly encoding blocks of N symbols a data stream with a matrix to form a precoded data stream, wherein N is an integer function of the number of antennas N_(t) of a transmitter and an estimate number L of multi-path channels from the transmitter to a receiver; and transmitting the precoded data stream with the antennas. 